Let us consider Case (1) in Table 1 where we take \(\delta =1\) .
Note that in this case, when \(\mathbf {K}_{N}\)  is diagonal one will obtain
the usual \(N\) -soliton solutions, which coincide with those results that have been obtained from
the inverse scattering transform (or Riemann-Hilbert method)
[1]}, [2]}, [3]}, [4]},
dressing method [5]},
Darboux transformation [6]}, [7]}
with zero as a seed solution
and bilinear method by Matsuno [8]},
including the solutions for the FL equation (REF ) in light of the transformation
that converts Eq.(REF ) to Eq.(REF ) (see proposition 1 in [2]}).
Apart from the diagonal \(\mathbf {K}_{N}\) , when \(\mathbf {K}_{N}\)  is a Jordan matrix
or contains Jordan blocks, the solution, in principle,
can be obtained by a limit procedure from soliton solutions
(e.g. [10]}, [11]}).
